Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16812092 | C2 | semidirect |
| 3. #20292529 | C2 | semidirect |
| 4. #20292525 | C2 | semidirect |
| 5. #20292518 | C2 | semidirect |
| 6. #20292506 | C2 | semidirect |
| 7. #20292487 | C2 | semidirect |
| 8. C22×C42×C107 | C2 | semidirect |
| 50. C22×C4×C107 | D4 | semidirect |
| 107. C4×C107 | #123 | semidirect |
| 118. C107 | #2854 | semidirect |
| 121. C22×C42 | D107 | semidirect |
| 160. C22×C4 | D428 | semidirect |
| 227. C4 | #16812092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812092 | 2 |
| C2×#16812083 | 2 |
| #20292529 | 2 |
| #20292525 | 2 |
| #20292518 | 2 |
| #20292506 | 2 |
| #20292487 | 2 |
| C22×C42×C107 | 2 |
| #2854 | 107 |